As noted in [1]}, it is challenging to measure the \(^{16}\) O/\(^{18}\) O ratios accurately from medium resolution spectra. The \(^{12}\) C\(^{16}\) O and \(^{12}\) C\(^{18}\) O absorption bands can be contaminated by absorption from other molecules such as \(^{12}\) C\(^{14}\) N and C\(_{2}\) . The absorption lines of CN and C\(_{2}\)  are densely packed in the K-band. It is also possible that the \(^{12}\) C\(^{16}\) O absorption bands are saturated, resulting in a smaller measured \(^{16}\) O/\(^{18}\) O ratios than the true value. There is also a degeneracy between the effects of the effective temperatures and nitrogen abundances on the depths of the CO absorption bands. For these reasons, we are not able to tightly constrain \(^{16}\) O/\(^{18}\) O, but instead provide a range of values combining the effects of the temperatures, nitrogen abundances and f\(_{\rm {dust}}\) . Wherever possible, we use estimates of temperatures from the literature to tighten the constraints. Despite the wide range of ratios for each star, our measurements conclusively show that most dLHdC stars have a significantly lower \(^{16}\) O/\(^{18}\) O than RCB stars.
